Finite Group DatabasebetaFinite Group Databasebeta| order | 32116 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C37 · Schur multiplier (H2) = C1 |
| direct product | C37×Dic217 |
| unambiguous semidirect product | C7⋊(C37×Dic31) |
| unambiguous semidirect product | C31⋊(Dic7×C37) |
| derived, Hall | C7×C31 ⋊ C4×C37 |
| Hall | C7×C31×C37 ⋊ C4 |
| Hall | C31×C37 ⋊ Dic7 |
| Hall | C7×C37 ⋊ Dic31 |
| Sylow | C31 ⋊ Dic7×C37 |
| Sylow | C7 ⋊ C37×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C37 | D217 |
| commutator, hypocenter | C7×C31 | C4×C37 |
| Frattini | C2 | C37×D217 |
| Fitting, socle, prime radical | C2×C7×C31×C37 | C2 |
| cosocle | C2×C7×C31 | C2×C37 |
| LCS | G ▷ C7×C31 | |
| UCS | C1 ◁ C2×C37 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32116 |
8140 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32116, 7);